📚 Year 10 Eduqas Engineering: Formula & Theorem Quick Reference Handbook | Year 10 Eduqas 工程：公式定理速查手册
This quick reference handbook gathers the essential formulas and theorems you will encounter in Year 10 Eduqas GCSE Engineering. It covers mechanics, materials, electricity, fluid power and machine systems. Each entry is presented with a concise explanation in English, followed by the Chinese translation, to help you revise and apply key concepts effectively.
这本速查手册汇集了 Year 10 Eduqas GCSE 工程中需要掌握的基本公式和定理，主题涵盖力学、材料、电学、流体动力与机械系统。每个条目先给出英文讲解，再附中文翻译，帮助你高效复习并灵活运用这些核心知识点。
1. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force about a pivot. It is calculated by multiplying the force by the perpendicular distance from the pivot to the line of action of the force.
力矩是力绕支点产生的转动效应。其大小等于力与支点到力作用线的垂直距离的乘积。
M = F × d
M is the moment in newton-metres (N·m), F is the force in newtons (N), and d is the perpendicular distance in metres (m).
M 表示力矩，单位为牛顿·米 (N·m)；F 为力，单位牛顿 (N)；d 为垂直距离，单位米 (m)。
Levers are simple machines that use a pivot to amplify an input force. In a Class 1 lever the pivot lies between the effort and the load; in Class 2 the load is between the pivot and the effort; in Class 3 the effort is between the pivot and the load.
杠杆是一种利用支点放大输入力的简单机械。一级杠杆的支点在施力点和负载之间；二级杠杆的负载在支点和施力点之间；三级杠杆的施力点在支点和负载之间。
When an object is in rotational equilibrium, the total clockwise moment equals the total anticlockwise moment about the same pivot.
当物体处于转动平衡时，绕同一点的所有顺时针力矩之和等于所有逆时针力矩之和。
Σ Mcw = Σ Macw
This principle is used to calculate unknown forces in lever systems, beams and structures.
这一原理常用于求解杠杆系统、横梁和结构中的未知力。
2. Mechanical Advantage & Velocity Ratio | 机械效益与速度比
Mechanical advantage (MA) tells you how much a machine multiplies the effort force. It is the ratio of the load to the effort.
机械效益 (MA) 表示机械将输入力放大了多少倍。它是负载与施力的比值。
MA = Load ÷ Effort
Velocity ratio (VR) describes the relationship between the distance moved by the effort and the distance moved by the load in the same time (or for one cycle).
速度比 (VR) 描述在同一时间（或一个循环内）施力移动的距离与负载移动的距离之比。
VR = deffort ÷ dload
For an ideal machine with no friction, MA equals VR. In real machines, MA is always less than VR because of energy losses.
在无摩擦的理想机械中，MA 等于 VR。而在实际机械中，由于能量损失，MA 总是小于 VR。
In a lever, VR can also be found from the ratio of the effort arm to the load arm.
对于杠杆，速度比也可以通过施力臂与负载臂的长度比计算。
VR = effort arm ÷ load arm
3. Efficiency | 效率
Efficiency measures how well a machine converts input energy into useful output work. It is expressed as a percentage.
效率衡量机械将输入能量转化为有用输出功的程度，通常以百分比表示。
η = (useful work output ÷ total energy input) × 100%
η (eta) is the symbol for efficiency. You can also calculate efficiency using power values.
η（eta）是效率的符号。你也可以使用功率值计算效率。
η = (useful power output ÷ total power input) × 100%
In mechanical systems, efficiency can be linked to MA and VR: η = MA ÷ VR × 100%.
在机械系统中，效率可以与 MA 和 VR 关联：η = MA ÷ VR × 100%。
Energy is often lost as heat due to friction, air resistance or electrical resistance. Engineers aim to maximise efficiency to save energy and reduce costs.
能量常因摩擦、空气阻力或电阻而以热的形式散失。工程师力求最大限度地提高效率，从而节约能源并降低成本。
4. Stress, Strain & Young’s Modulus | 应力、应变与杨氏模量
Stress measures the internal force per unit area within a material when an external force is applied.
应力衡量材料受外力时单位面积上所产生的内力。
σ = F ÷ A
σ (sigma) is the stress in pascals (Pa) or N/m², F is the applied force in newtons (N), and A is the cross-sectional area in m².
σ 为应力，单位帕斯卡 (Pa) 或 N/m²；F 为施加的力 (N)；A 为横截面积 (m²)。
Strain is the extension per unit length and has no units.
应变是单位长度上的伸长量，无量纲。
ε = ΔL ÷ L0
ε (epsilon) is strain, ΔL is the change in length and L0 is the original length.
ε 为应变，ΔL 是长度变化量，L0 是原始长度。
Young’s modulus (E) describes the stiffness of a material in the elastic region. It is the gradient of the stress-strain graph up to the limit of proportionality.
杨氏模量 (E) 描述材料在弹性范围内的刚度，是应力-应变曲线在比例极限内直线的斜率。
E = σ ÷ ε
E is measured in pascals (Pa). A high Young’s modulus means the material is stiff; a low value means it is flexible.
E 的单位是帕斯卡 (Pa)。杨氏模量越高，材料越刚硬；越低则越柔软。
5. Ohm’s Law & Electrical Power | 欧姆定律与电功率
Ohm’s law relates the voltage across a conductor to the current flowing through it and its resistance.
欧姆定律描述了导体两端电压与流过电流及电阻之间的关系。
V = I × R
V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω).
V 为电压，单位伏特 (V)；I 为电流，单位安培 (A)；R 为电阻，单位欧姆 (Ω)。
Electrical power is the rate at which electrical energy is transferred. It can be calculated in several ways.
电功率是电能传递的速率，有多种计算方式。
P = V × I
P = I2 × R
P = V2 ÷ R
P is power in watts (W). The appropriate formula is chosen depending on the known quantities.
P 为功率，单位瓦特 (W)。可根据已知量选择合适的公式。
In engineering, these formulas are essential for selecting the correct cable sizes, fuses and components in circuits.
在工程中，这些公式对于选择正确的导线规格、熔断器和电路元件至关重要。
6. Series & Parallel Resistors | 串联与并联电阻
When resistors are connected in series, the total resistance is the sum of the individual resistances.
当电阻串联时，总电阻等于各个电阻之和。
Rtotal = R1 + R2 + R3 + …
In a series circuit, the current is the same through all components, but the voltage splits across them.
在串联电路中，通过所有元件的电流相同，但电压会分配在各个元件上。
For resistors in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances.
对于并联电阻，总电阻的倒数等于各支路电阻倒数之和。
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …
In a parallel circuit, the voltage across each branch is the same, while the total current is the sum of the branch currents.
在并联电路中，各支路两端的电压相同，而总电流等于各支路电流之和。
Combining resistors in series and parallel allows engineers to design circuits with the desired total resistance and current distribution.
工程师通过串并联电阻的组合，可以设计出具有所需总电阻和电流分配方式的电路。
7. Work, Energy & Power | 功、能量与功率
Work is done when a force moves an object in the direction of the force.
当力使物体沿力的方向移动时，力就对物体做了功。
W = F × d
W is work in joules (J), F is the force in newtons (N), and d is the distance moved in metres (m).
W 为功，单位焦耳 (J)；F 为力 (N)；d 为移动距离 (m)。
Gravitational potential energy (GPE) is the energy an object has due to its height above the ground.
重力势能 (GPE) 是物体因其离地高度而具有的能量。
GPE = m × g × h
m is mass (kg), g is gravitational field strength (≈9.8 N/kg on Earth), and h is height (m).
m 为质量 (kg)；g 为重力场强度（地球约 9.8 N/kg）；h 为高度 (m)。
Kinetic energy (KE) is the energy of a moving object.
动能 (KE) 是运动物体所具有的能量。
KE = ½ × m × v2
v is the velocity in metres per second (m/s).
v 为速度，单位米/秒 (m/s)。
Power is the rate of doing work or transferring energy.
功率是做功或能量转换的速率。
P = W ÷ t
P is power in watts (W), t is time in seconds (s). For a vehicle moving at constant speed, power can also be found from P = F × v.
P 为功率 (W)；t 为时间 (s)。对于匀速运动的车辆，功率也可用 P = F × v 计算。
8. Gear & Pulley Systems | 齿轮与滑轮系统
Gears transmit rotary motion and can change speed, torque and direction. The gear ratio is determined by the number of teeth on the gears.
齿轮传递旋转运动，并能改变转速、扭矩和方向。齿轮比由齿数决定。
Gear ratio = Tdriven ÷ Tdriver
The output speed of a simple gear train is given by:
简单齿轮系的输出转速计算公式为：
Nout = Nin × (Tdriver ÷ Tdriven)
Where N represents rotational speed (rpm) and T the number of teeth. If the driven gear has more teeth, the output speed decreases and torque increases (ignoring friction).
其中 N 代表转速 (rpm)，T 为齿数。如果从动轮齿数更多，输出转速降低而扭矩增大（忽略摩擦）。
For a pulley system, the velocity ratio equals the number of rope sections that support the load.
对于滑轮系统，速度比等于支撑负载的绳段数。
VR = n
where n is the number of load-bearing ropes. The mechanical advantage depends on friction and rope stiffness but is always less than or equal to VR.
n 为承载绳段数。机械效益因摩擦和绳索刚度而异，但总是小于或等于 VR。
MA = Load ÷ Effort ≤ VR
9. Hydraulics & Pneumatics | 液压与气动
Pressure in a fluid is defined as force per unit area.
流体中的压强定义为单位面积上的力。
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